Kolloquiumsvortrag Mathematik: A short introduction to set optimization

Abstract: This talk gives a short introduction to multiobjective and set optimization and to the different possibilities to define optimal solutions for such problems. We start with a special set optimization problem which arises in case of a robust approach to decision uncertainty in optimization. This occurs when values of decision variables cannot be put into practice exactly. Then, for each feasible point, we have to consider the set of all of its possible realizations. Thus, one has to compare sets instead of points. These sets may just be intervals in case of a scalar-valued objective function, or may have a more complicated structure in case the decision uncertainty appears in a multiobjective optimization problem. We define optimality for such problems and we discuss how these special concepts are related to optimality notions in set optimization. We also give an overview over related concepts in set optimization based on different set relations and discuss their practical relevance. First approaches to determine solutions of such problems are also presented.